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We are given the following information:

- \( R \) is the midpoint of \( QS \).
- \( RS = 2x - 4 \),
- \( ST = 4x - 1 \),
- \( RT = 8x - 43 \).

To find \( QS \), we will use the fact that \( R \) is the midpoint of \( QS \), meaning \( QR = RS \).

### Steps:

1. Since \( R \) is the midpoint, \( QR = RS = 2x - 4 \).

2. The total length of \( RT \) can be written as:
   \[
   RT = QR + RS + ST = (2x - 4) + (2x - 4) + (4x - 1).
   \]

3. Simplifying:
   \[
   RT = (2x - 4) + (2x - 4) + (4x - 1) = 8x - 9.
   \]

4. We are also given that \( RT = 8x - 43 \), so we can set up the equation:
   \[
   8x - 9 = 8x - 43.
   \]

5. Solving for \( x \):
   \[
   8x - 9 = 8x - 43,
   \]
   Subtract \( 8x \) from both sides:
   \[
   -9 = -43.
   \]

This is a contradiction. Let's recheck the problem. Since we used the given information and got a contradiction, it's likely there's an inconsistency in the question's provided values.

Would you like further clarification, or perhaps check if some information is missing?

If R is the midpoint of QS, RS = 2x - 4, ST = 4x - 1, and RT = 8x - 43, find QS.

In this problem, we use algebra to find the length of QS, given that R is the midpoint. We also utilize the properties of midpoints and line segments to solve for x. The problem involves the expressions RS = 2x - 4, ST = 4x - 1, and RT = 8x - 43. Suitable for students in Grades 9-10.

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